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oai:recercat.cat:2117/204582025-07-17T00:01:50Zcom_2072_1033col_2072_452950

Hyperbolic uniformizations throught computations on ternary quadratic forms Alsina Aubach, Montserrat Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres Àrees temàtiques de la UPC::Matemàtiques i estadística Fuchsian groups Embeddings (Mathematics) Forms, Quadratic Quaternions Fuchsian groups, quaternion algebras, quadratic forms, embeddings Fuchsian, Grups de Formes quadràtiques Quaternions Orders in indefinite quaternion algebras provide Fuchsian groups acting on the Poincare half-plane, used to construct the associated Shimura curves. We explain how, by using embedding theory, the elements of those Fuchsian groups depend on representations of integers by suitable ternary quadratic forms. Thus the explicit computation of those representations leads to explicit presentations and fundamental domains of those Fuchsian groups, the computation of CM points, and a rich interpretation of the points in the complex upper half-plane. Peer Reviewed Postprint (published version) 2013 Conference report Alsina, M. Hyperbolic uniformizations throught computations on ternary quadratic forms. A: Applications of Computer Algebra. "Proceedings of Applications of Computer Algebra. ACA 2013. Ed.: José Luis Galán, Gabriel Aguilera and Pedro Rodríguez". Málaga: 2013, p. 203-206. 978-84-616-4565-7 https://hdl.handle.net/2117/20458 eng http://www.aca2013.uma.es/Proceedings.pdf http://creativecommons.org/licenses/by/3.0/es/ Open Access Attribution 3.0 Spain 4 p. application/pdf